Let the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Define A = {1, 2, 3, 4, 5} and B = {2, 4, 6, 8}. Which of the following represents the set (A ∩ B) ∪ (A \ B)?
Show the answer and explanation
Correct answer
A. {1, 2, 3, 4, 5}
Principle or equation
For sets A and B, A ∩ B is the intersection (elements in both), A \ B is the set difference (elements in A but not in B). The union combines all elements from both sets without duplication.
Why this answer is correct
A = {1, 2, 3, 4, 5}, B = {2, 4, 6, 8}. Then A ∩ B = {2, 4}. A \ B = {1, 3, 5}. The union of {2, 4} and {1, 3, 5} is {1, 2, 3, 4, 5}, which is exactly A. Therefore the correct answer is {1, 2, 3, 4, 5}.
Example
If A = {1,2,3} and B = {2,3,4}, then A ∩ B = {2,3}, A \ B = {1}, and (A ∩ B) ∪ (A \ B) = {1,2,3} = A.
This published item includes a stored explanation and passed the platform’s publication workflow. It is independent preparation material, not a claim of an official or recalled examination question.